Suppose that a stock price has an expected return of $16 \%$ per annum and a volatility of $30 \%$ per annum. When the stock price at the end of a certain day is $$\$ 50$$, calculate the following:
(a) The expected stock price at the end of the next day
(b) The standard deviation of the stock price at the end of the next day
(c) The $95 \%$ confidence limits for the stock price at the end of the next day.